%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SET822-2 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% Computer : n014.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri Sep 25 02:48:40 PM UTC 2026
% Result : Unsatisfiable 1.75s 1.29s
% Output : CNFRefutation 1.75s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 7
% Syntax : Number of formulae : 23 ( 12 unt; 1 def)
% Number of atoms : 44 ( 9 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 33 ( 19 ~; 14 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 5 ( 3 usr; 2 prp; 0-3 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-3 aty)
% Number of variables : 38 ( 0 sgn 38 !; 0 ?; 25 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] : ~ c_in(X0,c_emptyset,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OemptyE_0) ).
fof(f2,axiom,
! [X2,X0,X1] : c_in(X0,c_insert(X0,X1,X2),X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OinsertCI_1) ).
fof(f3,axiom,
! [X2,X3,X0,X1] :
( X0 = X1
| c_in(X0,X2,X3)
| ~ c_in(X0,c_insert(X1,X2,X3),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OinsertE_0) ).
fof(f4,negated_conjecture,
v_P(v_f(v_b)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).
fof(f5,negated_conjecture,
! [X0,X1] :
( c_in(v_x(X0,X1),X1,tc_IntDef_Oint)
| ~ c_in(v_f(X0),X1,tc_IntDef_Oint) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_1) ).
fof(f6,negated_conjecture,
! [X0,X1] :
( ~ v_P(v_x(X0,X1))
| ~ c_in(v_f(X0),X1,tc_IntDef_Oint) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_2) ).
tcf(c_55,plain,
! [X0: $i,X1: $i] : ~ c_in(X0,c_emptyset,X1),
inference(cnf_transformation,[],[f1]) ).
tcf(c_56,plain,
! [X0: $i,X1: $i,X2: $i] : c_in(X0,c_insert(X0,X1,X2),X2),
inference(cnf_transformation,[],[f2]) ).
tcf(c_57,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( c_in(X0,X2,X3)
| ( X0 = X1 )
| ~ c_in(X0,c_insert(X1,X2,X3),X3) ),
inference(cnf_transformation,[],[f3]) ).
tcf(c_58,negated_conjecture,
v_P(v_f(v_b)),
inference(cnf_transformation,[],[f4]) ).
tcf(c_59,negated_conjecture,
! [X0: $i,X1: $i] :
( c_in(v_x(X0,X1),X1,tc_IntDef_Oint)
| ~ c_in(v_f(X0),X1,tc_IntDef_Oint) ),
inference(cnf_transformation,[],[f5]) ).
tcf(c_60,negated_conjecture,
! [X0: $i,X1: $i] :
( ~ v_P(v_x(X0,X1))
| ~ c_in(v_f(X0),X1,tc_IntDef_Oint) ),
inference(cnf_transformation,[],[f6]) ).
tcf(c_104,plain,
! [X0: $i,X1: $i] :
( ~ c_in(v_f(X0),X1,tc_IntDef_Oint)
| ( v_x(X0,X1) != v_f(v_b) ) ),
inference(resolution_lifted,[status(thm)],[c_58,c_60]) ).
tcf(c_149,definition,
iPr_def_10 = v_f(v_b),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_150,plain,
! [X0: $i,X1: $i] :
( ~ c_in(v_f(X0),X1,tc_IntDef_Oint)
| ( v_x(X0,X1) != iPr_def_10 ) ),
inference(demodulation,[status(thm)],[c_104,c_149]) ).
tcf(c_151,negated_conjecture,
! [X0: $i,X1: $i] :
( c_in(v_x(X0,X1),X1,tc_IntDef_Oint)
| ~ c_in(v_f(X0),X1,tc_IntDef_Oint) ),
inference(demodulation,[status(thm)],[c_59]) ).
tcf(c_261,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_in(v_x(X0,c_insert(X1,X2,tc_IntDef_Oint)),X2,tc_IntDef_Oint)
| ( v_x(X0,c_insert(X1,X2,tc_IntDef_Oint)) = X1 )
| ~ c_in(v_f(X0),c_insert(X1,X2,tc_IntDef_Oint),tc_IntDef_Oint) ),
inference(superposition,[status(thm)],[c_151,c_57]) ).
tcf(c_272,plain,
! [X0: $i,X1: $i] :
( ( v_x(X0,c_insert(X1,c_emptyset,tc_IntDef_Oint)) = X1 )
| ~ c_in(v_f(X0),c_insert(X1,c_emptyset,tc_IntDef_Oint),tc_IntDef_Oint) ),
inference(superposition,[status(thm)],[c_261,c_55]) ).
tcf(c_286,plain,
! [X0: $i] : v_x(X0,c_insert(v_f(X0),c_emptyset,tc_IntDef_Oint)) = v_f(X0),
inference(superposition,[status(thm)],[c_56,c_272]) ).
tcf(c_292,plain,
v_x(v_b,c_insert(iPr_def_10,c_emptyset,tc_IntDef_Oint)) = iPr_def_10,
inference(superposition,[status(thm)],[c_149,c_286]) ).
tcf(c_298,plain,
~ c_in(v_f(v_b),c_insert(iPr_def_10,c_emptyset,tc_IntDef_Oint),tc_IntDef_Oint),
inference(superposition,[status(thm)],[c_292,c_150]) ).
tcf(c_301,plain,
~ c_in(iPr_def_10,c_insert(iPr_def_10,c_emptyset,tc_IntDef_Oint),tc_IntDef_Oint),
inference(light_normalisation,[status(thm)],[c_298,c_149]) ).
tcf(c_302,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_301,c_56]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET822-2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.11/0.37 % Computer : n014.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Thu Sep 24 12:03:33 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.11/0.41 Running first-order theorem proving
% 0.11/0.41 Running: /export/starexec/sandbox/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.43
% 0.11/0.43 % ======== iProver multi-core TPTP/SMT =========
% 0.11/0.43
% 0.11/0.43 % Detected problem language: tptp
% 0.11/0.44 % Proving...
% 1.75/1.29 % SZS status Started for theBenchmark.p
% 1.75/1.29 % SZS status Unsatisfiable for theBenchmark.p
% 1.75/1.29
% 1.75/1.29 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 1.75/1.29
% 1.75/1.29 % ------ iProver source info
% 1.75/1.29
% 1.75/1.29 % git: date: 2026-07-19 20:42:38 +0200
% 1.75/1.29 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 1.75/1.29 % git: non_committed_changes: false
% 1.75/1.29
% 1.75/1.29 % ------ Parsing...% successful
% 1.75/1.29
% 1.75/1.29
% 1.75/1.29 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 1.75/1.29
% 1.75/1.29 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe:1:0s pe_e sup_sim: 0 sf_s rm: 2 0s sf_e pe_s pe_e %
% 1.75/1.29
% 1.75/1.29 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 1.75/1.29
% 1.75/1.29 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 1.75/1.29 % ------ Proving...
% 1.75/1.29 % ------ Problem Properties
% 1.75/1.29
% 1.75/1.29 %
% 1.75/1.29 % clauses 6
% 1.75/1.29 % conjectures 1
% 1.75/1.29 % EPR 1
% 1.75/1.29 % Horn 5
% 1.75/1.29 % unary 3
% 1.75/1.29 % binary 2
% 1.75/1.29 % lits 10
% 1.75/1.29 % lits eq 3
% 1.75/1.29 % fd_pure 0
% 1.75/1.29 % fd_pseudo 0
% 1.75/1.29 % fd_cond 0
% 1.75/1.29 % fd_pseudo_cond 1
% 1.75/1.29 % AC symbols 0
% 1.75/1.29
% 1.75/1.29 % ------ Schedule dynamic 5 is on
% 1.75/1.29
% 1.75/1.29 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 1.75/1.29
% 1.75/1.29
% 1.75/1.29 % ------
% 1.75/1.29 % Current options:
% 1.75/1.29 % ------
% 1.75/1.29
% 1.75/1.29
% 1.75/1.29 %
% 1.75/1.29
% 1.75/1.29 % ------ Proving...
% 1.75/1.29 %
% 1.75/1.29
% 1.75/1.29 % SZS status Unsatisfiable for theBenchmark.p
% 1.75/1.29
% 1.75/1.29 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 1.75/1.29
% 1.75/1.29
%------------------------------------------------------------------------------